Surface Methodology
3. Results and Discussion 1. Statistical Analyses
In this section, the effect of FA content, sliding speed and applied load on wear rate and coefficient of friction are discussed. RSM was applied to evaluate and develop models of wear rate and friction coefficient of AA6063-FA composites.
In an attempt to obtain a model with better performance than the one given by the quadratic model of the process, a cubic model equation was developed, but owing to the fact that the developed cubic model was found to be aliased in nature, its model expression in terms of the actual factors was not given by the Design Expert. However, the aliased cubic model, the mathematical expression of which was not available, was still analyzed for variance to see if actually increasing order of model had any effect on the response statistically.
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The models summary statistics given in Tables5and6show that the quadratic models were suggested according to the statistical evaluation of different models. The software also revealed that the cubic order model was aliased for the ranges of the data obtained. The quadratic model was used according to the value of R-squared (0.9791, 0.9818) for wear rate and coefficient of friction model respectively.
Table 5.Statistical summary of wear rate model.
Source Std.
Dev. R-Squared Adjusted R-Squared
Predicted
R-Squared PRESS Recommendation
Linear 0.60 0.9437 0.9401 0.9338 19.76
2FI 0.48 0.9656 0.9609 0.9548 13.50
Quadratic 0.39 0.9791 0.9745 0.9658 10.20 Suggested
Cubic 0.36 0.9858 0.9784 0.9633 10.97 Aliased
Table 6.Statistical Summary of Coefficient of Friction Model.
Source Std.
Dev. R-Squared Adjusted R-Squared
Predicted
R-Squared PRESS Recommendation
Linear 0.024 0.9214 0.9164 0.9043 0.033
2FI 0.020 0.9483 0.9412 0.9242 0.026
Quadratic 0.012 0.9818 0.9778 0.9699 0.010 Suggested
Cubic 0.009406 0.9915 0.9872 0.9769 0.007958 Aliased
3.2. Modeling and Analysis of Variance of Wear Rate
The design of experiment software with response surface method was used to statistically study the effect of fly ash (FA), sliding speed (S) and applied load (L) on the wear rate of AA6063-FA composites and to build an empirical model for Wear rate based on the effects of these factors. The sequential F-test was conducted for testing the significance of the regression model.
The step-wise regression method was utilized for the wear rate model with the entire potential combinations of the control factors with exception of the cubic terms since these terms were aliased for the data ranges obtained. The selected terms along with the step-wise regression method led to the elimination of the less significant model terms automatically. Table7shows the analysis of variance generated for wear rate model. The model F-value of 213.395 confirms the significance of the model.
Ap-value of 0.0001 was indicative that there was a low chance of F-value which could occur as result of noise. The predicted R2of 0.9658, which represent the measure of the amount of variation about the mean explained by the model agrees well with the adjusted R2of 0.9745. The adjusted R2and predicted R2should be within approximately 0.20 of each other so as to be in agreement, or else setbacks may arise with either the data or the model. High R2value suggest there is a statistically significant interaction between factors. Resulting wear rate within the investigated ranges of parameters can be modeled by the final equation produced, Equation (5).
Wr=0.037685− 0.10651× FA+0.054471 ×S+0.019936 ×L − 0.001056× FA× S
−0.00337143 ×FA ×L+0.0000796096× S× L+0.0070058 ×FA2−0.0000709692× S2+ 0.000880987 ×L2
(5)
The order of the factors influencing the wear rate can be established through analysis of the F-value magnitude as follows: it can be observed the F-value of FA (837.432) was the most significant parameter having the highest statistical influence on the wear rate of AA6063-FA composites followed by applied load (483.037) and sliding speed (286.805) and S, which implies that the FA content has greater effect on wear rate value than the L and S factor.
Adequate precision ratio, which represent the signal-to-noise ratio, with values higher than 4 indicate adequate model discrimination [17]. It compares the range between the predicted values at
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the design points to the average prediction error. As shown in Table7, the adequate ratio was 59.006, which indicates that the model has capacity of navigating the design space. The R2value of about 0.9791 indicates the variability of the response was 97.91% about the mean which proved the model provide a good fit for the data. This fact alongside with the remarkable residual analysis led to the conclusion that the model given in Equation (5) can predict the wear rate of the compound within the investigated range of all three parameters.
Table 7.ANOVA results for the quadratic model of wear rate.
Sum of Mean F p-Value
Source Squares df Square Value Prob>F
Model 292.32 9 32.48 213.39 <0.0001 Significant
A-weight fraction 127.46 1 127.46 837.43 <0.0001
B-sliding speed 43.65 1 43.65 286.80 <0.0001
C-Load 73.52 1 73.52 483.04 <0.0001
AB 1.36 1 1.36 8.96 0.0047
AC 3.49 1 3.49 22.95 <0.0001
BC 0.20 1 0.20 1.30 0.2600
A2 0.48 1 0.48 3.18 0.0819
B2 0.35 1 0.35 2.33 0.1348
C2 3.17 1 3.17 20.83 <0.0001
Residual 6.24 41 0.15
Cor Total 298.56 50
Std. Dev. 0.39 R-squared 0.9791
Mean 7.63 Adj R-squared 0.9745
C.V. % 5.11 Pred R-squared 0.9658
PRESS 10.20 Adequate Precision 59.006
Furthermore, in Table7, both theSL(BC) andS2(B2) terms are considered to be insignificant as theirp-value was greater than 0.05. However, these terms were automatically added in order to support the model’s hierarchy. In contrast, it is evident that the combined interaction of FA×L has the strongest effect on the response. The essential effects of the parameters on the responses, i.e., wear rate and the coefficient of friction, are further illustrated using contour lines and 3D surface plots.
Graphical Results of Wear Rate Model
Figure1presents the variance of collected data points about the linearized line which relates the predicted values with the actual values. This observation clearly indicates the model provide a good fit for the wear rate response.
Figure2further presents the perturbation plot of the wear rate data at the experimented mid values of the process parameters. The comparison of the effects of all three parameters at a specific area in the design range can be enabled by the perturbation plot. The response (wear rate) was graphically plotted by changing a single parameter over its investigated limits while other parameters were maintained constant. Similar to the significance of thep-value, this tool was also effective in identifying the interactive effects of parameters on the response [17]. The X-axis of the plot showed the relative position of the chosen levels of the parameters to the coded scale. The slopes of the curves showed the rate at which the parameter influenced the response. In Figure2, the point selected in the design range was the central point (FA=6 wt%, S 200 rpm and L 49 N).
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Figure 1.Experimental versus predicted wear rate mm3/m.
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Design-Expert® Software Factor Coding: Actual Wear rate (mm3/m) Actual Factors A: weight fraction = 6 B: sliding speed = 200 C: Load = 49
Figure 2.Perturbation plot of the effect of Fly ash content, sliding speed and applied load on wear rate of AA6063-FA composites.
The plot indicates that the fly ash content FA has the strongest inverse proportion (negative slope) on the wear rate while the load L has a smaller effect than FA, which was a direct proportional one (positive slope). The quadratic curves depicting the influence of the parameters on the wear rate were attributed to the quadratic terms in the model.
In summary, it is evident from Figure2that the FA content has negative effect on wear rate while both the applied load and sliding speed exhibit a positive impact on the wear rate. By increasing the FA content, the wear rate can be decreased while the opposite can be obtained when the applied load and sliding speed were increased. This trend was similar to that obtained from the experimental results.
The combined effects of two process parameters on the wear rate, while the third was kept constant, were further evaluated and these are demonstrated in Figures3–5. As described earlier for the perturbation plot, the third parameter could be changed, but again, it was kept at similar value selected for the perturbation figure. The red spheres on the graphs represent the experimental data points. Moreover, it is evident, especially on the 3D plots, that these spheres have close location to the
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surfaces, which indicate that the model fits properly with the data points. With respect to the effects of the combined parameters, they portrayed similar findings to those presented in the perturbation plot. However, by identifying their effects relative to the numerical values of the response, they offer a visual aid in selecting the desired ranges of the parameters. Furthermore, they were important in the optimization process of the ranges of the processing parameters so as to meet certain response criteria.
Owing to these facts and to avoid redundancy, only brief discussions were given for each figure as provided in the following paragraph.
Figure3a shows the contour plot of the effect of S and FA on the wear rate Wr. Each contour curve showed combinations of the two parameters that will predict a constant wear rate value. This wear rate value was observed inside the box situated at the middle of each contour curve. From the contour plot, S has a direct proportional effect on the predicted wear rate, while FA was inversely proportionate.
The same data are further illustrated in 3D plot as shown in Figure3b. The 3D plot has the added advantage of visual display of the effect of one of the parameter changes when the value of the other parameter is modified. For instance, consider the effect of S at two different values of FA which were at 0- and 12-wt%, it can be observed that the FA effect was stronger in the first case.
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Figure 4.View of the interactive effect of S and L on the Wr (a) contour lines 2D, (b) 3D.
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Figure 5.FA and L contour showing the interactive effect on Wr, (a) contour lines, (b) 3D.
Figure4a,b present that both S and L have directly proportional effects on the Wr. However, L has stronger effect than S. This indicated that variations in L led to larger variations in the Wr than those emanating from large variations in S.
Figure5a,b shows that FA has an inversely proportional effect on the Wr, while L has a directly proportional effect. Similarly, FA has stronger effect on the response than L exhibits.
3.3. Modeling and Analysis of Variance for Coefficient of Friction
Likewise, the previous analyses described in Section3.2were repeated for the case of the coefficient of friction response. Again, the step-wise regression method was employed with the entire potential combinations of all three parameters and similarly too, the cubic terms were aliased for the ranges of the data obtained. The selection of the terms alongside the step wise regression method resulted in the elimination of the negligible model terms automatically [17]. Table8summarizes the computed ANOVA results with the variance for the Coefficient of friction model and all terms in the model.
Table 8.ANOVA for Response Surface Quadratic model (coefficient of friction model).
Sum of Mean F p-Value
Source Squares df Square Value Prob>F
Model 0.34 9 0.038 245.70 <0.0001 Significant
A-Fly ash content 0.19 1 0.19 1219.47 <0.0001
B-Load 0.069 1 0.069 451.39 <0.0001
C-Sliding speed 0.061 1 0.061 399.07 <0.0001
AB 6.376×10−3 1 6.376×10−3 41.61 <0.0001
AC 1.054×10−3 1 1.054×10−3 6.88 0.0122
BC 5.305×10−4 1 5.305×10−4 3.46 0.0700
A2 0.010 1 0.010 66.91 <0.0001
B2 1.049×10−3 1 1.049×10−3 6.85 0.0124
C2 2.273×10−5 1 2.273×10−5 0.15 0.7021
Residual 6.282×10−3 41 1.532×10−4
Cor Total 0.35 50
Std. Dev. 0.012 R-squared 0.9818
Mean 0.24 Adj R-squared 0.9778
C.V.% 5.23 Pred R-squared 0.9699
PRESS 0.010 Adeq Precision 66.605
In Table8, it is shown that combined interaction of FA×L also had the strongest effects on the coefficient of friction. The effect of the parameters on the response is further demonstrated via the contour and 3D surface plots. The S2and SL terms were proven to be insignificant as evidenced from
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thep-value which was greater than 0.05. Nonetheless, this term again was also to support the model hierarchy. The step-wise regression method detected that this model term was insignificant however, it was necessary by other significant model terms. Moreover, in Table8, the adequacy measures of R2, adjusted R2and predicted R2were near to 1; they all agree well which is indicative of sufficient model [23]. The adequacy precision was greater than 4 which indicated sufficient model discrimination.
In addition, this shows that the model has the capacity of navigating the design space [17]. The R2 value of approximately 0.9818 implies that around 98.18 of the data variability can be substantiated by model. Again, similarly to the wear rate, the model was proven to be a very good fit to the data and that the coefficient of friction, within the range of parameters investigated, can be predicted.
Equation (6) presents the process model estimated from the experimental results within the range of parameters investigated.
Fr=0.74823−0.040431×FA−0.00516264×L−0.00103544×S+0.000144033×FA×L+
0.0000293612×FA×S+0.00000411498×S×L+
0.00101923×FA2+0.0000160301×L2+0.00000056855×S2
(6)
In summary, the model described by Equation (6) can provide good predictions of the coefficient of friction through any combinations of the fly ash content, sliding speed and load, within the range investigated.
Graphical Results of Coefficient of Friction
Figure6presents the variance of data points about the linearized line relating the actual and predicted values, which is an indication of the good fitness value of the model.
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Figure 6.Actual versus predicted scattering of the data points.
For the process parameters, the perturbation (see Figure7) was obtained at a similar point of location (FA=6 wt%, S 200 rpm and L 49 N). From the figure, it is evident that FA has inversely proportional effect and has the maximum effect on the coefficient of friction. The second maximum effect was owing to L which also had an inversely proportional effect on the coefficient of friction.
The sliding speed also exhibited an inversely proportional effect.
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Figure 7.Perturbation plot of the process control variables’ effects on the coefficient of friction.
The following Figures8–10, present the combined influences of two parameters, at a time on Fr. the design points are represented by the red spheres on the graphs; their locations on the 3D plots was a confirmation that both the model and the data points have a good fit. The contour plot for the influence of FA and S on Fris presented in Figure8a. It is evident from the contour plot that S and FA have an inversely proportional effect on Fr. It can be observed from the 3D plot in Figure8b that as FA and S decrease the Frdecreases. By employing the combination of low S and low FA settings, the deepest Frvalues were generated, while holding L constant, in this case at its mid-range=49 N.
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Figure 8.View of the interactive effect of FA and S on Fr, (a) contour lines 2D, (b) 3D.
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Figure 9.FA and L contour showing the interactive effect on the Fr, (a) contour lines 2D, (b) 3D.
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Figure 10.View of the interactive effect of S and L on Fr, (a) contour lines 2D, (b) 3D.
Figure9a,b indicates that both FA and L have an inversely proportional influence on the Fr. Nonetheless, FA exhibited stronger effect than L. Slight changes in FA often affect the Frin a magnitude greater than changes caused by even large changes in L.
Figure10a,b shows that S and L have an inversely proportional effect on the Fr. In a similar way, S, which can be evidenced from the slopes of the contour lines and 3D surface, almost exhibited equal to L effect on the Fr.
3.4. Validation of the Statistical Models
The wear rate and coefficient of friction were numerically modeled by RSM based on FA content, applied load and sliding speed. Thereafter, the statistical model was validated with a dataset, 20% from the experimental data were used in the process of models building to verify the produced models and find the reliability of the model and the measured responses were recorded.
The predicted wear rate and coefficient of friction calculated by Equations (5) and (6) were plotted against experimental data in Figures11and12. The figures indicated that the surface response method model provides excellent coincidence with experimental value with R-squared value of 0.9665 and
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0.9893 respectively. These results were expected due to the high order model used in SRM which provide more accurate response.
5ð
Wr pred, mm3/m
Wr exp, mm3/m
Figure 11.SRM-predicted wear rate versus experimental results.
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Fr pred
Fr exp
Figure 12.SRM-predicted coefficient of friction versus experimental results.
4. Conclusions
AA6063 alloy-based aluminum matrix composites with FA particles have been successfully fabricated with compocasting technique. The overall results revealed that the wear resistance of the composites was positively enhanced by the inclusion of the FA particles. The wear resistance enhancement was attributed to increased hardness, generation of strain fields, homogenous distribution, spherical shape of FA particles and reduction in effective contact area. Increasing FA content restricted the deformation of the matrix material. The wear rates of the composites were increased by the applied load. FA content exhibited an inversely proportional relationship with wear rate, coefficient of friction and friction force for AA6063-FA composites. Increasing the sliding speed increased the wear rate but decreased the coefficient of friction and friction force of composites. In addition, the wear rate and fractional force of composites increased with increasing applied load, but coefficient of friction varied inversely with applied load. These control parameters were then employed to build statistical models for the wear rate and coefficient of friction. FA had the highest statistical influence on the wear rate and coefficient of friction of AA6063-FA composites followed by applied load and sliding speed.
Moreover, FA content with applied load exhibited the strongest interaction effects. Finally, AA6063
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aluminum matrix composites reinforced with FA can be used in applications that require excellent wear resistance.
Author Contributions:The research conceptualization and methodology are contributed by A.M.R., D.L.M. and U.M.B.; the experimental and numerical works including the data curation are performed by A.M.R. and U.M.B.;
the results analysis and interpretation are conducted by A.M.R., D.L.M., U.M.B. and M.R.I.; the preparation of the original draft, reviews and editing are contributed by A.M.R. and D.L.M. and lastly the project administration, supervision and funding are managed by D.L.M. All authors have read and agreed to the published version of the manuscript.
Funding:The authors would like to acknowledge the financial support from the Ministry of Education Malaysia with reference code FRGS/1/2019/STG07/UPM/02/10 and Vot No. 5540209.
Conflicts of Interest:The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
Nomenclature
min Minute
rpm Revolution per minute
ASTM American Society for Testing and Materials
FA Fly ash
Al Aluminum
AA6063 AA6063 aluminum alloy
AA6063-FA AA6063 aluminum alloy-fly ash composites MMCs Metal matrix composites
AMCs Aluminum matrix composites AMMCs Aluminum metal matrix composites
Al-FA Aluminum–fly ash
B4C Boron carbide
Graphite Gr
XRD X-ray diffraction
XRF X-ray fluorescence
ANOVA Analysis of variance RSM Response surface method
DRAMCs Discontinuously reinforced aluminum matrix composites DOE Design of experimental
CCD Based central composite design
SS Semisolid-semisolid
SL Semisolid-liquid
Wr Wear rate (mm3/m)
Fr Coefficient of friction
μ The coefficient of friction FT Tangential force (N)
FN Normal force (N)
V Volume loss (mm3)
S Sliding speed (rpm)
L Applied load (N)
Wrp Predicted wear rate
Frp Predicted coefficient of friction Wre Experimental wear rate
Fre Experimental coefficient of friction Wra Average of experimental wear rate
Fra Average of experimental coefficient of friction vol% Percentage of volume fraction
wt% Percentage of weight fraction